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\section{Materials and Methods}


\subsection{Sampling}

Thirty two trees from 17 species were sampled in different locations in the Lorraine region around Nancy (north-eastern France). For each species one tree of good external commercial quality and the other one of poor external quality were selected.

For each sample tree, five one-meter-long logs were sampled: three logs (L2, L4, L6) with fixed heights in the trunk (1.5 to 2.5 m, 3.5 to 4.5 m, and 5.5 to 6.5 m), and two logs with tree-dependent heights, one of which (LC1) was taken just under the crown base, and the other (LC2) at the base of the upper half of the crown.

A total of 141 logs from this sample (one to five per tree) were analysed in this study (Table \ref{tableEssences}).

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*****Table \ref{tableEssences} about here*****
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\subsection{X-ray CT scanning}
% ARRANGER : copié/collé de Haykel

The logs were scanned using a medical X-ray device devoted to materials such as wood or soil. Scanning was performed after several months of air-drying since CT images of wet wood are usually poorly contrasted. The disadvantage of this long storage time was that drying checks sometimes appeared at log ends. The exact moisture content at scanning time was not measured.

The logs were scanned with the X-ray generator set to 80 kV - 50 mA.
Slice thickness and the interval between slices were set to 1.25 mm. The reconstruction process was performed using a DETAIL filter\footnote{One of the seven reconstruction filters available with the scanner software. The DETAIL filter is very similar to the STANDARD filter but slightly more noisy.} with a pixel size of 0.20 to 0.98 mm, depending on the log diameter (2.6 to 36.0 cm) and shape\footnote{The field of view was chosen so as to be close to the bounding box of the log or slightly bigger.}, and resulted in a stack of $512 \times 512$ images of the slices saved in the medical DICOM format (\url{http://medical.nema.org}). Due to the fact that numeric images are discrete, we were aware that the best possible accuracy in terms of location in the image corresponded to the pixel size. Image grey levels are given in Hounsfield units and can be converted to density values (in $kg \cdot m^{-3}$) by adding an offset of approximately 1000 \citep{Freyburger2009}.

\subsection{Manual measurements from CT images}
% ARRANGER : copié/collé de Haykel

Knot data were recorded on each log using ImageJ software \citep {Imagej2010} and a plug-in dedicated to the analysis of internal tree architecture by X-ray CT scanning (\textit{Gourmands} plug-in, described in \citet {Colin2010}). The operator reviews the image stack and manually places markers along the pith. The software linearly interpolates the pith position between two markers and outputs the resulting coordinates for each slice. Since the interpolated results are displayed in real-time, the operator may move the markers or add new ones at any moment for a more accurate tracking of the pith trajectory.

The knot shape and size were manually recorded using ImageJ software \citep {Imagej2010}. A plug-in dedicated to the analysis of internal tree architecture by X-ray CT scanning (\textit{Gourmands} plug-in, described in \citet {Colin2010}) was used. The method consists in navigating through the image stack and manually place markers along knots and bud traces to record their location and shape. Different markers were used for coding the following features: sequential knot (Ks), epicormic knot (Ke), trace of bud of primary (B1) or secondary (B2) origin, trace of adventive bud (Ba). The trajectory of the pith was also recorded. For sequential and epicormic knots two lines of markers were used, the mid-line giving the trajectory of the knot and the distance between the two lines giving the diameter profile, assuming a circular cross section. 

\subsection{Computation of variables}

Based on the software outputs the following variables were used in this study:
	\begin{itemize}
	\item \textbf{Relative length} of a knot or bud trace: ratio of the horizontal length to the mean log radius;
	\item \textbf{Relative maximal diameter} of a knot: ratio of the maximal knot diameter to the mean log diameter;
	\item \textbf{Diameter decrease} of a knot: ratio of the diameter at the knot end to the maximal knot diameter (below 1 value means that the knot reaches a maximal diameter before decreasing);
	\item \textbf{Initial inclination angle} of a knot: angle between the horizontal plane and the line linking the knot starting point (near the pith) to a point located 5 cm farer on the trajectory (positive value means that the knot is raising up).
	\end{itemize}

Basic statistics of the distribution of these variables were computed on each log.
For describing the arrangement of leaves on a log, knots and buds of primary origin (Ks and B1) were first grouped in clusters. Two successive knots or buds vertically distant from less than 10 mm were assumed to belong to the same cluster. 
The angle between the first elements of two consecutive clusters was computed for each log, and the mode of the obtained distribution was supposed to estimate the \textbf{phyllotactic angle}. The \textbf{rate of clusters} per meter and the modal value of the distribution of \textbf{cluster size} was also computed for each log.

Table  \ref{tableVariables} summarizes the variables finally used in the classification after removing highly correlated variables.

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*****Table \ref{tableVariables} about here*****
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